Compare the prices of both the 350D and the 20D and see what you like. Also, I'd say that you should give Nikon a shot as well. Try the D70 and D70s. Other brands like Olympus, Pentax and the [supposedly gone] Konica Minolta also offer good systems but I've read too little about them to know. Consider what film SLRs you have used in the past and then choose a brand from there since it might be easier to learn the ropes. Or else, read lots of reviews and get a feel for what is available.
Whichever one you take, stick to the kit lens first, which is the lens that comes with your camera. Do lots of shooting in a variety of locations and then decide if you usually want a wider lens or a longer one. If the kit lens has just the right shooting range for you, then upgrade sometime down the track. Don't rush into buying ANY lenses though...sit back, read books, reviews and ask for comments on these forums to see what people have to say. Most photography purchases are expensive and cannot be taken lightly. :sweatsm: And to think that I should know better.
It may seem difficult to upgrade from film to digital, but it is not. Soon you will feel the advantages of digital, especially if you like instant results. However, post-processing images at the computer using Photoshop might take a while to learn. I won't go into an argument between digital and film, because both have their advantages. Both will also take a while to learn. ISO is the same concept as that of film ASA rating.
Shoot lots, and you'll soon know your stuff.